The present work discusses the proposal of a spintronic neuromorphic system with spin orbit torque driven domain wall motion-based neuron and synapse. We propose a voltage-controlled magnetic anisotropy domain wall motion based magnetic tunnel junction neuron. We investigate how the electric field at the gate (pinning site), generated by the voltage signals from pre-neurons, modulates the domain wall motion, which reflects in the non-linear switching behaviour of neuron magnetization. For the implementation of synaptic weights, we propose 3-terminal MTJ with stochastic domain wall motion in the free layer. We incorporate intrinsic pinning effects by creating triangular notches on the sides of the free layer. The pinning of domain wall and intrinsic thermal noise of device lead to the stochastic behaviour of domain wall motion. The control of this stochasticity by the spin orbit torque is shown to realize the potentiation and depression of the synaptic weight. The micromagnetics and spin transport studies in synapse and neuron are carried out by developing a coupled micromagnetic Non-Equilibrium Green’s Function (MuMag-NEGF) model. The minimization of the writing current pulse width by leveraging the thermal noise and demagnetization energy is also presented. Finally, we discuss the implementation of digit recognition by the proposed system using a spike time dependent algorithm.